login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047606 Numbers that are congruent to {1, 2, 3, 5} mod 8. 1
1, 2, 3, 5, 9, 10, 11, 13, 17, 18, 19, 21, 25, 26, 27, 29, 33, 34, 35, 37, 41, 42, 43, 45, 49, 50, 51, 53, 57, 58, 59, 61, 65, 66, 67, 69, 73, 74, 75, 77, 81, 82, 83, 85, 89, 90, 91, 93, 97, 98, 99, 101, 105, 106, 107, 109, 113, 114, 115, 117, 121, 122, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

From Bruno Berselli, Jul 17 2012: (Start)

G.f.: x*(1+x+x^2+2*x^3+3*x^4)/((1+x)*(1-x)^2*(1+x^2)).

a(n) = 2*n-3+(3-(-1)^n)*(1-i^(n*(n+1)))/4, where i=sqrt(-1). (End)

From Wesley Ivan Hurt, Jun 02 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(2k) = A047617(k), a(2k-1) = A047471(k). (End)

E.g.f.: (6 + 2*sin(x) - cos(x) + 4*(x - 1)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, Jun 03 2016

MAPLE

A047606:=n->2*n-3+(3-I^(2*n))*(1-I^(n*(n+1)))/4: seq(A047606(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

MATHEMATICA

Select[Range[120], MemberQ[{1, 2, 3, 5}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 5, 9}, 60] (* Bruno Berselli, Jul 17 2012 *)

PROG

From Bruno Berselli, Jul 17 2012: (Start)

(MAGMA) [n: n in [1..120] | n mod 8 in [1, 2, 3, 5]];

(Maxima) makelist(2*n-3+(3-(-1)^n)*(1-%i^(n*(n+1)))/4, n, 1, 60);

(PARI) Vec((1+x+x^2+2*x^3+3*x^4)/((1+x)*(1-x)^2*(1+x^2))+O(x^60)) (End)

CROSSREFS

Cf. A047471, A047617.

Sequence in context: A058314 A072735 A127149 * A226826 A047370 A226820

Adjacent sequences:  A047603 A047604 A047605 * A047607 A047608 A047609

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 19:59 EST 2019. Contains 320403 sequences. (Running on oeis4.)